document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=300795>Question 300795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a tough time solving this problem, any help would be much appreciated.\r<BR>\n" );
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document.write( "solve an inequality (x)/(x+20)>(2)/(x+8)\r<BR>\n" );
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document.write( "A. (-&#8734;,-10) (-10,-8) (4,&#8734;)<BR>\n" );
document.write( "B. (-&#8734;,-8) (4,&#8734;)<BR>\n" );
document.write( "C. (-10,-8)<BR>\n" );
document.write( "D. (-20,-10) (-8,-4)<BR>\n" );
document.write( "E. (-&#8734;,-20) (-10,-8) (4,&#8734;)\r<BR>\n" );
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document.write( "I came up with E but I'm not sure if the answer is correct. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #215767 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=215767\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29 ALIGN=MIDDLE  ALT=\"%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Look at the inequality and determine when the left hand side equals the right hand side. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%29%2F%28x%2B20%29=%282%29%2F%28x%2B8%29 ALIGN=MIDDLE  ALT=\"+%28x%29%2F%28x%2B20%29=%282%29%2F%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B8%29=2%28x%2B20%29 ALIGN=MIDDLE  ALT=\"x%28x%2B8%29=2%28x%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x=2x%2B40 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x=2x%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x-40=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x-40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can factor this quadratic,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B10%29%28x-4%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B10%29%28x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-10 ALIGN=MIDDLE  ALT=\"x=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In addition, because of the x terms in the denominator, add the additional points when the denominator goes to zero. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-20 ALIGN=MIDDLE  ALT=\"x=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set up a number line and break it up using these two points.<BR>\n" );
document.write( "Region 1: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-20 ALIGN=MIDDLE  ALT=\"+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( " Region 2: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20 ALIGN=MIDDLE  ALT=\"-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-10 ALIGN=MIDDLE  ALT=\"+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Region 3: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10 ALIGN=MIDDLE  ALT=\"-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8 ALIGN=MIDDLE  ALT=\"+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Region 4: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Region 5: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+infinity ALIGN=MIDDLE  ALT=\"+infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Choose points in each region and check the inequality in that region to see if it's valid or not. \r<BR>\n" );
document.write( "\n" );
document.write( "Region 1: Pick <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-30 ALIGN=MIDDLE  ALT=\"x=-30\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29 ALIGN=MIDDLE  ALT=\"%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-30%29%2F%28-30%2B20%29%3E%282%29%2F%28-30%2B8%29 ALIGN=MIDDLE  ALT=\"%28-30%29%2F%28-30%2B20%29%3E%282%29%2F%28-30%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-30%2F-10%3E2%2F-22 ALIGN=MIDDLE  ALT=\"-30%2F-10%3E2%2F-22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%3E-1%2F11 ALIGN=MIDDLE  ALT=\"3%3E-1%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, Region 1 is a valid region.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Region 2: Pick <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-15 ALIGN=MIDDLE  ALT=\"x=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-15%29%2F%28-15%2B20%29%3E%282%29%2F%28-15%2B8%29 ALIGN=MIDDLE  ALT=\"%28-15%29%2F%28-15%2B20%29%3E%282%29%2F%28-15%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-15%29%2F%285%29%3E%282%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"%28-15%29%2F%285%29%3E%282%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%3E-%282%2F7%29 ALIGN=MIDDLE  ALT=\"-3%3E-%282%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "False, Region 2 is not a valid region.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Region 3: Pick x=-9.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29 ALIGN=MIDDLE  ALT=\"%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%29%2F%28-9%2B20%29%3E%282%29%2F%28-9%2B8%29 ALIGN=MIDDLE  ALT=\"%28-9%29%2F%28-9%2B20%29%3E%282%29%2F%28-9%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F11%3E-2 ALIGN=MIDDLE  ALT=\"9%2F11%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, Region 3 is  a valid region.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Region 4: Pick x=0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29 ALIGN=MIDDLE  ALT=\"%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3E%282%29%2F%280%2B8%29 ALIGN=MIDDLE  ALT=\"0%3E%282%29%2F%280%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3E1%2F4 ALIGN=MIDDLE  ALT=\"0%3E1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "False, Region 4 is not a valid region.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Region 5: Pick x=10.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29 ALIGN=MIDDLE  ALT=\"%28x%29%2F%28x%2B20%29%3E%282%29%2F%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F30%3E2%2F18 ALIGN=MIDDLE  ALT=\"10%2F30%3E2%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3%3E1%2F9 ALIGN=MIDDLE  ALT=\"1%2F3%3E1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, Region 5 is a valid region.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-20 ALIGN=MIDDLE  ALT=\"+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >)U(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10 ALIGN=MIDDLE  ALT=\"-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8 ALIGN=MIDDLE  ALT=\"+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >)U(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+infinity ALIGN=MIDDLE  ALT=\"+infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "E is the correct answer.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );